[R-sig-ME] Understanding variance components

Chen, Gang (NIH/NIMH) [C] gangchen at mail.nih.gov
Thu Jan 5 17:28:15 CET 2017

Suppose that I have the following dataset in R:

mydata <- Machines[Machines$Machine!='C’,]

With the following model:

print(lmer(score ~ 1 + (1|Worker/Machine), data=mydata), ranef.comp="Var")

I have the variance components as shown below:

Random effects:
 Groups         Name        Variance
 Machine:Worker (Intercept) 46.00   
 Worker         (Intercept) 13.84   
 Residual                    1.16   

I have trouble understanding exactly what the first two components are: Machine:Worker and Worker? Specifically,

1) What is the variance for Worker: corresponding to the base (or reference) level of the factor Machine? If so, what is the base level: the first level in the dataset or alphabetically the first level (it happens to be the same in this particular dataset)?

2) What is the variance for Machine:Worker? Is it the variance for the second level of the factor Machine, or the extra variance relative to the variance for Worker?

Furthermore, for the model:

print(lmer(score ~ 1 + (1|Worker/Machine), data=Machines), ranef.comp="Var")

what is the variance for Machine:Worker in the following result since there are 3 levels involved in the factor Machine?

Random effects:
 Groups         Name        Variance
 Machine:Worker (Intercept) 60.2972 
 Worker         (Intercept)  7.3959 
 Residual                    0.9246 


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